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- W4282587919 abstract "We prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (that is, non-classical) twist of K $K$ -theory over G = S U ( n ) $G=SU(n)$ . This twist is represented by a Fell bundle E → G $mathcal {E}rightarrow mathcal {G}$ , which reduces to the basic gerbe for the top exterior power functor. The groupoid G $mathcal {G}$ comes equipped with a G $G$ -action and an augmentation map G → G $mathcal {G}rightarrow G$ , that is an equivariant equivalence. The C ∗ $C^*$ -algebra C ∗ ( E ) $C^*(mathcal {E})$ associated to E $mathcal {E}$ is stably isomorphic to the section algebra of a locally trivial bundle with stabilised strongly self-absorbing fibres. Using a version of the Mayer–Vietoris spectral sequence, we compute the equivariant higher twisted K $K$ -groups K ∗ G ( C ∗ ( E ) ) $K^G_*(C^*(mathcal {E}))$ for arbitrary exponential functor twists over S U ( 2 ) $SU(2)$ , and also over S U ( 3 ) $SU(3)$ after rationalisation." @default.
- W4282587919 created "2022-06-14" @default.
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- W4282587919 date "2022-06-01" @default.
- W4282587919 modified "2023-10-17" @default.
- W4282587919 title "Equivariant higher twisted K$K$‐theory of SU(n)$SU(n)$ for exponential functor twists" @default.
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- W4282587919 doi "https://doi.org/10.1112/topo.12219" @default.
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